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TMF, 2010, Volume 165, Number 1, Pages 3–24 (Mi tmf6560)  

This article is cited in 9 scientific papers (total in 9 papers)

The equivalence of different approaches for generating multisoliton solutions of the KPII equation

M. Boitia, F. Pempinellia, A. K. Pogrebkovb, B. Prinariac

a Dipartimento di Fisica, Universitáa del Salento and Sezione, INFN, Lecce, Italy
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
c Department of Mathematics, University of Colorado, Colorado Springs, USA

Abstract: The unexpectedly rich structure of the multisoliton solutions of the KPII equation has previously been explored using different approaches ranging from the dressing method to twisting transformations and the $\tau$-function formulation. All these approaches proved useful for displaying different properties of these solutions and the corresponding Jost solutions. The aim of our investigation is to establish explicit formulas relating all these approaches. We discuss some hidden invariance properties of these multisoliton solutions.

Keywords: KPII equation, Bäcklund transformation, tau function, soliton

DOI: https://doi.org/10.4213/tmf6560

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English version:
Theoretical and Mathematical Physics, 2010, 165:1, 1237–1255

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Received: 11.03.2010

Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “The equivalence of different approaches for generating multisoliton solutions of the KPII equation”, TMF, 165:1 (2010), 3–24; Theoret. and Math. Phys., 165:1 (2010), 1237–1255

Citation in format AMSBIB
\by M.~Boiti, F.~Pempinelli, A.~K.~Pogrebkov, B.~Prinari
\paper The~equivalence of different approaches for generating multisoliton solutions of the~KPII equation
\jour TMF
\yr 2010
\vol 165
\issue 1
\pages 3--24
\jour Theoret. and Math. Phys.
\yr 2010
\vol 165
\issue 1
\pages 1237--1255

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    This publication is cited in the following articles:
    1. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Properties of the solitonic potentials of the heat operator”, Theoret. and Math. Phys., 168:1 (2011), 865–874  mathnet  crossref  crossref  mathscinet  isi
    2. Boiti M., Pempinelli F., Pogrebkov A.K., “Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions”, J Math Phys, 52:8 (2011), 083506  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. V. S. Gerdjikov, “Two-dimensional Toda field equations related to the exceptional algebra $\mathfrak g_2$: Spectral properties of the Lax operators”, Theoret. and Math. Phys., 172:2 (2012), 1085–1096  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Extended resolvent of the heat operator with a multisoliton potential”, Theoret. and Math. Phys., 172:2 (2012), 1037–1051  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    5. Zarmi Ya., “Nonlinear Quantum-Dynamical System Based on the Kadomtsev-Petviashvili II Equation”, J. Math. Phys., 54:6 (2013), 063515  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Zarmi Ya., “Vertex Dynamics in Multi-Soliton Solutions of Kadomtsev-Petviashvili II Equation”, Nonlinearity, 27:6 (2014), 1499–1523  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Gerdjikov V.S., Smirnov A.O., Matveev V.B., “From Generalized Fourier Transforms to Spectral Curves For the Manakov Hierarchy. i. Generalized Fourier Transforms”, Eur. Phys. J. Plus, 135:8 (2020), 659  crossref  isi
    8. Wu D., “The Direct Scattering Problem For the Perturbed Gr(1,2)(> 0)Kadomtsev-Petviash-Vili II Solitons”, Nonlinearity, 33:12 (2020), 6729–6759  crossref  mathscinet  isi
    9. Biondini G., Hoefer M.A., Moro A., “Integrability, Exact Reductions and Special Solutions of the Kp-Whitham Equations”, Nonlinearity, 33:8 (2020), 4114–4132  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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